Eliezer presents a strong defence of the correspondence theory? Well, for some values of “strong”. He puts forward the best possible example of correspondence working clearly and obviously, and leaves the reader with the impression that it works as well in all cases. In fact, the CToT is not universally accepted because there are a number of cases where it is hard to apply. One of them is maths’n’logic, the ostensible subject of your posting,
I would have thought that the outstanding problem with the correspondence theory of truth in relation to maths is: what do true mathematical statements correspond to? Ie, what is the ontology of maths? You seem to offer only the two sentences:-
“Mathematical statements are true when they are truth-preserving, or valid. They’re also conditional: they’re about all possible causal fabrics rather than any one in particular”
The first is rather vague. Truth preservation is a property of connected chains of statements. Such arguements are valid when and only when they are truth preserving, because that is how validity is defined in this context. The conclusion of a mathematical argument is true when it’s premises are true AND when it is valid (AKA truth preserving). Validity is not a vague synonym for truth: the extra condition about the truth of the premises is important.
Are mathematical statements about all possible causal fabrics? Is “causal fabric” a meaningful term? Choose one.
If a causal fabric is a particular kind of mathematical structure, a directed acyclic graph, for instance, then it isn’t the only possible topic of mathematics, it’s too narrow a territory, …maths can be about cyclic or undirected graphs, for instance.
On the other hand, if the phrase “causal fabric” doesn’t constrain anything, then what is the territory...what does it do...and how you tell it is there? Under the standard correspondence of truth as applied to empirical claims, a claim is true if a corresponding piece of territory exists, and false if doesn’t. But how can a piece of the mathematical territory go missing?
Mathematical statements are proven by presenting deductions from premises, ultimately from intuitively appealing axioms. We can speak of the set of proven and proveable theorems as a territory, but that establishes only a superficial resemblance to correspondence: examined in detail, the mathematical map-territory relationship works in reverse. It is the existence of a lump of physical territory that proves the truth of the corresponding claim; whereas the truth of a mathematical claim is proved non empirically, and the idea that it corresponds to some lump of metaphorical mathspace is conjured up subsequently.
Is that too dismissive of mathematical realism? The realist can insist that theorems aren’t true unless they correspond to something in Platonia...even if a proof has been published and accepted. But the idea that mathematicians, despite all their efforts, are essentially in the dark about mathematicall truth us quite a bullet to bite. The realist can respond that mathematicians are guided by some sort of contact between their brains and the non physical realm of Platonia, but that is not a claim a physicalist should subscribe to.
So , the intended conclusion is that no mathematical statement is made true by the territory, because there is no suitable territory to do so. Of course, the Law of the Excluded Middle, and the Principle of Non Contradiction are true in the systems that employ them, because they are axioms of the systems that employ them, and axioms are true by stipulation.
I agree with the examples you present to the effect that we need to pick and choose between logical systems according to the domain. I disagree with the conclusion that an abandonment of truth is necessary...or possible.
To assert P is equivalent to asserting “P is true” (the deflationary theory in reverse). That is still true if P is of the form “so and so works”. Pragmatism is not orthogonal to, or transcendent of, truth. Pragmatists need to be concerned about what truly works.
Two people might disagree because they are running on the same epistemology, but have a different impression of the evidence applying within that epistemology. Or they might disagree about the epistemology itself. That can still apply where they are disagreeing about what works. So adopting pragmatism doesn’t make object level concerns about truth vanish, and it doesnt make meta level concerns , epistemology , vanish either.
Mathematical theorems aren’t true univocally, by correspondence to a single territory, but they are true by stipulation, where they can be proven. Univocal truth is wrong, and pragmatism, as an alternative to truth, is wrong. What is right is contextual truth.
Everyone finds the PoNC persuasive, yet many people believe contradictory things...in a sense. What sense?
Consider:
A. Sherlock Holmes lives at 221b Baker Street.
B. Sherlock Holmes never lived, he’s a fictional character.
Most people would regard both of them as true … in different contexts, the fictional and the real life. But someone who believed two contradictory propositions in the same context really would be irrational.
That was a wonderful comment. I hope you don’t mind if I focus on the last part in particular. If you’d rather I addressed more I can accommodate that, although most of that will be signalling agreement.
To assert P is equivalent to asserting “P is true” (the deflationary theory in reverse). That is still true if P is of the form “so and so works”. Pragmatism is not orthogonal to, or transcendent of, truth. Pragmatists need to be concerned about what truly works.
I’ll note a few things in reply to this:
I’m fine with some conceptual overlap between my proposed epistemology and other epistemologies and vague memes.
You might want to analyse statements “P” as meaning/being equivalent to “P is true,” but I am not going to include any explication of “true” in my epistemology for that analysis to anchor itself to.
Continuing the above, part of what I am doing is tabooing “truth,” to see if we can formulate an epistemology-like framework without it.
What “truly works” is more of a feeling or a proclivity than a proposition, until of course an agent develops a model of what works and why.
What is right is contextual truth.
I agree with you here absolutely, modulo vocabulary. I would rather say that no single framework is universally appropriate (problem of induction) and that developing different tools for different contexts is shrewd. But what I just said is more of a model inspired by my epistemology than part of the epistemology itself.
You might want to analyse statements “P” as meaning/being equivalent to “P is true,” but I am not going to include any explication of “true” in my epistemology for that analysis to anchor itself to
Analysing P as “P is true” isn’t some peculiarity of mine: in less formal terms, to assert something is to assert it as true. To put forward claims, and persuade others that they should believe them is to play a truth game...truth is what one should believe,
So your epistemology can’t dispense with truth, but offers no analysis of truth, How useful is that?
Continuing the above, part of what I am doing is tabooing “truth,” to see if we can formulate an epistemology-like framework without it.
Tabooing truth, or tabooing “truth”? It is almost always possible to stop using a word, but continue referring to the concept by synonymous words or phrases. Doing without the concept is harder....doing without the use, the employment us harder still.
What “truly works” is more of a feeling or a proclivity than a proposition, until of course an agent develops amodel of what works and why.
Nothing works just because someone feels it does. The truth of something truly working us given by the territory.
What is right is contextual truth.
I agree with you here absolutely, modulo vocabulary. I would rather say that no single framework is universally appropriate (problem of induction)
Eliezer presents a strong defence of the correspondence theory? Well, for some values of “strong”. He puts forward the best possible example of correspondence working clearly and obviously, and leaves the reader with the impression that it works as well in all cases. In fact, the CToT is not universally accepted because there are a number of cases where it is hard to apply. One of them is maths’n’logic, the ostensible subject of your posting,
I would have thought that the outstanding problem with the correspondence theory of truth in relation to maths is: what do true mathematical statements correspond to? Ie, what is the ontology of maths? You seem to offer only the two sentences:-
“Mathematical statements are true when they are truth-preserving, or valid. They’re also conditional: they’re about all possible causal fabrics rather than any one in particular” The first is rather vague. Truth preservation is a property of connected chains of statements. Such arguements are valid when and only when they are truth preserving, because that is how validity is defined in this context. The conclusion of a mathematical argument is true when it’s premises are true AND when it is valid (AKA truth preserving). Validity is not a vague synonym for truth: the extra condition about the truth of the premises is important.
Are mathematical statements about all possible causal fabrics? Is “causal fabric” a meaningful term? Choose one.
If a causal fabric is a particular kind of mathematical structure, a directed acyclic graph, for instance, then it isn’t the only possible topic of mathematics, it’s too narrow a territory, …maths can be about cyclic or undirected graphs, for instance.
On the other hand, if the phrase “causal fabric” doesn’t constrain anything, then what is the territory...what does it do...and how you tell it is there? Under the standard correspondence of truth as applied to empirical claims, a claim is true if a corresponding piece of territory exists, and false if doesn’t. But how can a piece of the mathematical territory go missing?
Mathematical statements are proven by presenting deductions from premises, ultimately from intuitively appealing axioms. We can speak of the set of proven and proveable theorems as a territory, but that establishes only a superficial resemblance to correspondence: examined in detail, the mathematical map-territory relationship works in reverse. It is the existence of a lump of physical territory that proves the truth of the corresponding claim; whereas the truth of a mathematical claim is proved non empirically, and the idea that it corresponds to some lump of metaphorical mathspace is conjured up subsequently.
Is that too dismissive of mathematical realism? The realist can insist that theorems aren’t true unless they correspond to something in Platonia...even if a proof has been published and accepted. But the idea that mathematicians, despite all their efforts, are essentially in the dark about mathematicall truth us quite a bullet to bite. The realist can respond that mathematicians are guided by some sort of contact between their brains and the non physical realm of Platonia, but that is not a claim a physicalist should subscribe to.
So , the intended conclusion is that no mathematical statement is made true by the territory, because there is no suitable territory to do so. Of course, the Law of the Excluded Middle, and the Principle of Non Contradiction are true in the systems that employ them, because they are axioms of the systems that employ them, and axioms are true by stipulation.
I agree with the examples you present to the effect that we need to pick and choose between logical systems according to the domain. I disagree with the conclusion that an abandonment of truth is necessary...or possible.
To assert P is equivalent to asserting “P is true” (the deflationary theory in reverse). That is still true if P is of the form “so and so works”. Pragmatism is not orthogonal to, or transcendent of, truth. Pragmatists need to be concerned about what truly works.
Two people might disagree because they are running on the same epistemology, but have a different impression of the evidence applying within that epistemology. Or they might disagree about the epistemology itself. That can still apply where they are disagreeing about what works. So adopting pragmatism doesn’t make object level concerns about truth vanish, and it doesnt make meta level concerns , epistemology , vanish either.
Mathematical theorems aren’t true univocally, by correspondence to a single territory, but they are true by stipulation, where they can be proven. Univocal truth is wrong, and pragmatism, as an alternative to truth, is wrong. What is right is contextual truth.
Everyone finds the PoNC persuasive, yet many people believe contradictory things...in a sense. What sense?
Consider:
A. Sherlock Holmes lives at 221b Baker Street.
B. Sherlock Holmes never lived, he’s a fictional character.
Most people would regard both of them as true … in different contexts, the fictional and the real life. But someone who believed two contradictory propositions in the same context really would be irrational.
That was a wonderful comment. I hope you don’t mind if I focus on the last part in particular. If you’d rather I addressed more I can accommodate that, although most of that will be signalling agreement.
I’ll note a few things in reply to this:
I’m fine with some conceptual overlap between my proposed epistemology and other epistemologies and vague memes.
You might want to analyse statements “P” as meaning/being equivalent to “P is true,” but I am not going to include any explication of “true” in my epistemology for that analysis to anchor itself to.
Continuing the above, part of what I am doing is tabooing “truth,” to see if we can formulate an epistemology-like framework without it.
What “truly works” is more of a feeling or a proclivity than a proposition, until of course an agent develops a model of what works and why.
I agree with you here absolutely, modulo vocabulary. I would rather say that no single framework is universally appropriate (problem of induction) and that developing different tools for different contexts is shrewd. But what I just said is more of a model inspired by my epistemology than part of the epistemology itself.
Analysing P as “P is true” isn’t some peculiarity of mine: in less formal terms, to assert something is to assert it as true. To put forward claims, and persuade others that they should believe them is to play a truth game...truth is what one should believe,
So your epistemology can’t dispense with truth, but offers no analysis of truth, How useful is that?
Tabooing truth, or tabooing “truth”? It is almost always possible to stop using a word, but continue referring to the concept by synonymous words or phrases. Doing without the concept is harder....doing without the use, the employment us harder still.
Nothing works just because someone feels it does. The truth of something truly working us given by the territory.
Contextual truth is compatible with no truth?